Spectral–Energy Efficiency Tradeoff in Full-Duplex Two-Way Relay Networks

Owing to its high spectral efficiency (SE), two-way relaying (TWR) has aroused tremendous research interests. Recently, substantial progress in self-interference (SI) cancelation makes full-duplex (FD) TWR practical. For this new paradigm, analyzing spectral-energy efficiency (SE-EE) tradeoff is crucial, which has not been addressed in the existing works in the literature. In this paper, the SE-EE tradeoff in a FDTW relay network with amplify-and-forward (AF) relaying is studied by considering the residual SI at the relay. An optimization problem is formulated to maximize the EE under the SE requirement and the maximum transmission power constraints by adjusting the transmission power of the terminals and the amplification gain of the relay. A lower complexity iterative optimization algorithm is developed to solve the optimization problem. Simulation results show that: 1) the proposed algorithm can achieve optimal EE that is consistent to the one obtained by the exclusive searching method; 2) the FDTW relay network can achieve higher SE but lower optimal EE compared with the half-duplex (HD) one; and 3) the optimal EE is insensitive to the residual power of SI, when the relay is located near either terminal.